1. Field of the Invention
This invention, generally, relates to computer-aided design of electronic circuits, and more specifically, the invention relates to developing corner models for various classes of nonlinear systems.
2. Background Art
Computer aids for electronic circuit designers are becoming more and more popular. Examples of these computer aids include electronic circuit simulators such as the Simulation Program with Integrated Circuit Emphasis (SPICE) developed at the University of California, Berkeley (UC Berkeley), and various enhanced versions or derivatives of SPICE, such as, SPICE2 or SPICE3, HSPICE, PSPICE, and SPECTRE.
An electronic circuit may contain circuit elements such as resistors, capacitors, inductors, mutual inductors, transmission lines, diodes, bipolar junction transistors (BJT), junction field effect transistors (JFET), and metal-on-silicon field effect transistors (MOSFET), etc. A SPICE circuit simulator is a program that simulates the performance of electronic circuits. SPICE solves sets of non-linear differential equations in the frequency domain; steady state and time domain and can simulate the behavior of transistor and gate designs. In SPICE, a circuit is handled in a node/element fashion, i.e., the circuit is regarded as a collection of various elements (transistors, resistors, capacitors, etc.) and the elements are connected at nodes. Thus, each element must be modeled in order to simulate the entire circuit. Most SPICE circuit simulators have built in models for modeling semiconductor devices, and are set up so that the user need only specify model parameter values associated with the models.
Whether it is built-in or plug-in, a device model for a SPICE circuit simulator typically includes model equations and a set of model parameters, which are used to mathematically represent device characteristics of a device element under various bias conditions. For example, for a MOSFET device model, in DC and AC analysis, the inputs of the device model are the drain-to-source, gate-to-source, bulk-to-source voltages, and the device temperature, and the outputs are the various terminal currents. Therefore, the model parameters, along with the model equations in the device model, directly affect the final outcome of the terminal currents.
SPICE models are enabled by Monte Carlo simulation capability. To reduce simulation time, it is desirable to have a corner model. For a set of circuit performance targets that depend on statistical model parameters linearly (e.g., the first-order approximation of targets around an operating point), there exists a set of known corner model solutions (see U.S. Pat. No. 6,901,570 for “Method of Generating Optimum Skew Corners for a Compact Device Model”, issued May 31, 2005). For a set of nonlinear systems (in terms of their dependency on statistical model parameters), however, there have not been general and exact corner model solutions other than going to the second-order approximation (quadratic response surface) in the targets vs. statistical model parameter relationship.